Computational Fluid Dynamics at the ICMA (Institute of Computational Mathematics and Applications).

Abstract

Abstract : This research concerned three independent projects of ICMA (Institute of Computational Mathematics and Applications) personnel, each belonging to the general area of computational fluid dynamics. The first project dealt with the computation of stationary Navier-Stokes solutions using continuation methods. Error estimates for certain finite element solutions of continuation problems were derived and extensions to more general operators including the Navier-Stokes operator were investigated. Numerical methods for the detection of Hopf bifurcation were studied. The second project involved construction, analysis and implementation of efficient computer algorithms for the finite difference and finite element-dual variable discretization of the two-dimensional Navier-Stokes problems. Particular attention was given to finite element and finite differences discretization such problems that arise in combustor modeling. The third project sought to extend the dual variable reduction technique to various fluid models. This required the construction of a network analogue for the discrete difference equations along with an analysis of the fundamental matrix and dual variable transformation involved. (Author)